In the current work, I aim at finding this important missing piece for our holographic jigsaw puzzle. As we will see in the remain of this paper, the low energy effective field theory (EFT) for the holographic dark energy model is actually a massive gravity theory. A graviton has three polarisations, namely one scalar mode, and two tensor modes. The UV-IR correspondence eq. (REF ) stems from the strong coupling of the scalar mode above the energy scale where our effective field theory breaks down. One may get puzzled at this point as the Poincare symmetry in 4 dimensional space-time implies a massive spin-2 particle has 5 polarisations (including helicity 0, \(\pm 1\) , \(\pm 2\) ). However, the massive gravity theory that we are going to engage is different from the conventional one [1]}[2]}, as the global Lorentz invariance is broken on the cosmological background and thus a graviton does not necessary to be well equipped with 5 polarisations [3]}[4]}. See Ref. [5]}[6]} for two comprehensive reviews on the topic of massive gravity.
